Qunity: A Unified Language for Quantum and Classical Computing (Extended Version)

TL;DR

Qunity is a novel quantum programming language that unifies quantum and classical computing with a consistent syntax and semantics, enabling natural expression of quantum algorithms and their compilation to low-level circuits.

Contribution

It introduces a unified syntax and denotational semantics for quantum and classical computing, incorporating the BQP subroutine theorem for reversible quantum subroutines.

Findings

Qunity can express several quantum algorithms clearly.

The language can be compiled into OpenQASM circuits.

Guarantees programs are quantum mechanically valid.

Abstract

We introduce Qunity, a new quantum programming language designed to treat quantum computing as a natural generalization of classical computing. Qunity presents a unified syntax where familiar programming constructs can have both quantum and classical effects. For example, one can use sum types to implement the direct sum of linear operators, exception-handling syntax to implement projective measurements, and aliasing to induce entanglement. Further, Qunity takes advantage of the overlooked BQP subroutine theorem, allowing one to construct reversible subroutines from irreversible quantum algorithms through the uncomputation of "garbage" outputs. Unlike existing languages that enable quantum aspects with separate add-ons (like a classical language with quantum gates bolted on), Qunity provides a unified syntax and a novel denotational semantics that guarantees that programs are quantum mechanically valid. We present Qunity's syntax, type system, and denotational semantics, showing how it can cleanly express several quantum algorithms. We also detail how Qunity can be compiled into a low-level qubit circuit language like OpenQASM, proving the realizability of our design.